Research My research area is in algebraic number theory with connections to arithmetic geometry, algebraic topology, and group theory. I am specifically interested in Galois actions. Publications and preprints R. Davis, R. Pries, K. Wickelgren The Galois action on the lower central series of the fundamental group of the Fermat curve, submitted August 2018. R. Davis and R. Pries Cohomology groups of Fermat curves via ray class fields of cyclotomic fields, submitted July 2018. R. Davis and E. H. Goins Arithmetic of quaternion origami, May 2018. R. Davis A note on the procedure to find the generic polynomial of a quotient (closely following Adelmann), May 2018. R. Davis, R. Pries, V. Stojanoska, and K. Wickelgren The Galois action and cohomology of a relative homology group of Fermat curves, J. Algebra, 505: 33-69, 2018. See the Magma files of computuations for the paper. A.C. Cojocaru, R. Davis, A. Silverberg, and K.E. Stange, Arithmetic properties of the Frobenius traces defined by a rational abelian variety, with two appendices by J-P. Serre. International Mathematics Research Notices, vol. 2016, pages 1-46. R. Davis, R. Pries, V. Stojanoska, and K. Wickelgren Galois action on the homology of Fermat curves, Directions in Number Theory: proceedings of the 2014 WIN3 workshop, Springer XV, pages 57-86. R. Davis Images of metabelian Galois representations associated to elliptic curves Women in numbers 2: research directions in number theory, 29-46, Contemp. Math., 606, Centre Rech. Math. Proc., Amer. Math. Soc., Providence, RI, 2013. R. Davis (advisor N. Boston) Thesis (2013). A. Brouwer, R. Davis, A. Larkin, D. Studenmund, and C. Tucker Intrinsically S^1 3-linked graphs and other aspects of S^1 embeddings Rose-Hulman Institute of Technology Undergraduate Math Journal (2007).